Nonlinear macroscopic behavior of micro-fractured composite materials

In order to accurately determine the mechanical response of advanced composite materials, large deformations and related instability and bifurcation phenomena occurring at the microstructural scale must be taken into account [1-2]. In addition, heterogeneous composite materials are susceptible to microscopic damage processes in the form of matrix micro-cracking or debonding between different microconstituents. Micro-fractures, often involving self-contact phenomena between crack faces, interact with microscopic instability phenomena and may induce an unstable behavior in the homogenized material, often leading to a premature collapse. When microscopic damage and self-contact mechanisms are taken into account in coupling with microstructural instability phenomena, the computational cost increases so much to make a direct simulation of the actual composite solid, usually carried out meshing all heterogeneities in the structure by a finite element discretization, hard to be carried out. It is therefore preferable to determine the nonlinear response of a composite solid in terms of its homogenized properties, by adopting appropriate non-linear homogenization techniques able to accurately correlate the microstructural response with the macroscopic behavior. In this context the understanding and modeling of instability phenomena in coupling with micro-cracking and self-contact within the framework of homogenization procedures, represents a problem of central significance ([3-4]). An analysis of the nonlinear homogenized response of elastic composite materials under finite deformations is investigated by describing the composite material as a periodic microstructure containing microcracks in frictionless unilateral self-contact. Stability and uniqueness characteristics of the homogenized response along prescribed monotonic macro-strain paths are analyzed by using an updated Lagrangian formulation and by including the influence of micro-cracks and of frictionless self-contact between crack faces. The theoretical results are numerically illustrated by means of 2D finite element applications, pointing out the strong influence of micro-fracture and self-contact on the homogenized composite response.